We propose a refined version of the stochastic SEIR model for epidemic of the new corona virus SARS-Cov-2, causing the COVID-19 disease, taking into account the spread of the virus due to the regular infected individuals (transmission coefficient $\beta$), hospitalized individuals (transmission coefficient $l\beta$, $l>0$) and superspreaders (transmission coefficient ${\beta }^{\prime }$). The model is constructed from the corresponding ordinary differential model by introducing two independent environmental white noises in transmission coefficients for above mentioned classes - one noise for infected and hospitalized individuals and the other for superspreaders. Therefore, the model is defined as a system of stochastic differential equations driven by two independent standard Brownian motions. Existence and uniqueness of the global positive solution is proven, and conditions under which extinction and persistence in mean hold are given. The theoretical results are illustrated via numerical simulations.

我们针对新冠病毒 SARS-Cov-2 的流行提出了一个改进版的随机 SEIR 模型，它引起了 COVID-19 疾病，同时考虑到病毒因普通感染者而传播（传播系数$\beta$), 住院患者 (传播系数$升\beta$,$升>0$）和超级传播者（传播系数${\beta }^{‘}$). 该模型是从相应的普通微分模型构建的，通过在上述类别的传输系数中引入两个独立的环境白噪声——一个噪声用于受感染和住院的个体，另一个噪声用于超级传播者。因此，该模型被定义为由两个独立的标准布朗运动驱动的随机微分方程组。证明了全局正解的存在性和唯一性，并给出了均值保持的灭绝和持久性条件。理论结果通过数值模拟进行说明。